Euler's Formula V - E + F = 2 | Proof @ThinkTwiceLtu

Think Twice | Euler's Formula V - E + F = 2 | Proof @ThinkTwiceLtu | Uploaded June 2020 | Updated October 2024, 1 day ago.
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Proofs for two theorems used in this video:
► Polygon triangulation: youtube.com/watch?v=2x4ioToqe_c
► Area of a spherical triangle: youtube.com/watch?v=Y8VgvoEx7HY

Euler's polyhedron formula is one of the simplest and beautiful theorems in topology. In this video we first derive the formula for the area of a spherical polygon using two theorems proven in the previous two videos which are linked above. This result is then used to prove the fact that V-E+F = 2 is true for all convex polyhedra by projecting the polyhedron on the surface of the sphere and doing some algebraic manipulation.
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#mathematics #geometry #Euler

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